The warp factor \(A(y)\)  encodes the warped background geometry. In RS1 [1]}, in which the extra dimension is unstabilized, \(A(y) = k|y|\) , where \(k\)  is related to the spacetime curvature. The Goldberger-Wise mechanism [2]}, [3]} complicates the background geometry such that the specific form of \(A(y)\)  becomes dependent on the details of the mechanism's bulk scalar interactions. Crucially, the scalar (bulk and boundary) potential terms in \(\mathcal {L}_{\text{pot}}\)  are chosen such that the scalar field gains a \(y\) -dependent background field value, and the trade-off between the contributions to the action from bulk kinetic energy terms \(\mathcal {L}_{\Phi \Phi }\)  and the scalar potential(s) stabilize the size of the extra-dimension.
